/****************************************************************************
 *
 * Copyright 2016 Samsung Electronics All Rights Reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing,
 * software distributed under the License is distributed on an
 * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND,
 * either express or implied. See the License for the specific
 * language governing permissions and limitations under the License.
 *
 ****************************************************************************/

/*
 *  Multi-precision integer library
 *
 *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
 *  SPDX-License-Identifier: Apache-2.0
 *
 *  Licensed under the Apache License, Version 2.0 (the "License"); you may
 *  not use this file except in compliance with the License.
 *  You may obtain a copy of the License at
 *
 *  http://www.apache.org/licenses/LICENSE-2.0
 *
 *  Unless required by applicable law or agreed to in writing, software
 *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 *  See the License for the specific language governing permissions and
 *  limitations under the License.
 *
 *  This file is part of mbed TLS (https://tls.mbed.org)
 */

/*
 *  The following sources were referenced in the design of this Multi-precision
 *  Integer library:
 *
 *  [1] Handbook of Applied Cryptography - 1997
 *      Menezes, van Oorschot and Vanstone
 *
 *  [2] Multi-Precision Math
 *      Tom St Denis
 *      https://github.com/libtom/libtommath/blob/develop/tommath.pdf
 *
 *  [3] GNU Multi-Precision Arithmetic Library
 *      https://gmplib.org/manual/index.html
 *
 */

#if !defined(MBEDTLS_CONFIG_FILE)
#include "tls/config.h"
#else
#include MBEDTLS_CONFIG_FILE
#endif

#if defined(MBEDTLS_BIGNUM_C)

#include "tls/bignum.h"
#include "tls/bn_mul.h"

#include <string.h>

#if defined(MBEDTLS_PLATFORM_C)
#include "tls/platform.h"
#else
#include <stdio.h>
#include <stdlib.h>
#define mbedtls_printf     printf
#define mbedtls_calloc    calloc
#define mbedtls_free       free
#endif

/* Implementation that should never be optimized out by the compiler */
static void mbedtls_mpi_zeroize(mbedtls_mpi_uint *v, size_t n)
{
	volatile mbedtls_mpi_uint *p = v;
	while (n--) {
		*p++ = 0;
	}
}

#define ciL    (sizeof(mbedtls_mpi_uint))	/* chars in limb  */
#define biL    (ciL << 3)		/* bits  in limb  */
#define biH    (ciL << 2)		/* half limb size */

#define MPI_SIZE_T_MAX  ((size_t)-1)	/* SIZE_T_MAX is not standard */

/*
 * Convert between bits/chars and number of limbs
 * Divide first in order to avoid potential overflows
 */
#define BITS_TO_LIMBS(i)  ((i) / biL + ((i) % biL != 0))
#define CHARS_TO_LIMBS(i) ((i) / ciL + ((i) % ciL != 0))

/*
 * Initialize one MPI
 */
void mbedtls_mpi_init(mbedtls_mpi *X)
{
	if (X == NULL) {
		return;
	}

	X->s = 1;
	X->n = 0;
	X->p = NULL;
}

/*
 * Unallocate one MPI
 */
void mbedtls_mpi_free(mbedtls_mpi *X)
{
	if (X == NULL) {
		return;
	}

	if (X->p != NULL) {
		mbedtls_mpi_zeroize(X->p, X->n);
		mbedtls_free(X->p);
	}

	X->s = 1;
	X->n = 0;
	X->p = NULL;
}

/*
 * Enlarge to the specified number of limbs
 */
int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs)
{
	mbedtls_mpi_uint *p;

	if (nblimbs > MBEDTLS_MPI_MAX_LIMBS) {
		return (MBEDTLS_ERR_MPI_ALLOC_FAILED);
	}

	if (X->n < nblimbs) {
		if ((p = (mbedtls_mpi_uint *) mbedtls_calloc(nblimbs, ciL)) == NULL) {
			return (MBEDTLS_ERR_MPI_ALLOC_FAILED);
		}

		if (X->p != NULL) {
			memcpy(p, X->p, X->n * ciL);
			mbedtls_mpi_zeroize(X->p, X->n);
			mbedtls_free(X->p);
		}

		X->n = nblimbs;
		X->p = p;
	}

	return (0);
}

/*
 * Resize down as much as possible,
 * while keeping at least the specified number of limbs
 */
int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs)
{
	mbedtls_mpi_uint *p;
	size_t i;

	/* Actually resize up in this case */
	if (X->n <= nblimbs) {
		return (mbedtls_mpi_grow(X, nblimbs));
	}

	for (i = X->n - 1; i > 0; i--)
		if (X->p[i] != 0) {
			break;
		}
	i++;

	if (i < nblimbs) {
		i = nblimbs;
	}

	if ((p = (mbedtls_mpi_uint *) mbedtls_calloc(i, ciL)) == NULL) {
		return (MBEDTLS_ERR_MPI_ALLOC_FAILED);
	}

	if (X->p != NULL) {
		memcpy(p, X->p, i * ciL);
		mbedtls_mpi_zeroize(X->p, X->n);
		mbedtls_free(X->p);
	}

	X->n = i;
	X->p = p;

	return (0);
}

/*
 * Copy the contents of Y into X
 */
int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y)
{
	int ret;
	size_t i;

	if (X == Y) {
		return (0);
	}

	if (Y->p == NULL) {
		mbedtls_mpi_free(X);
		return (0);
	}

	for (i = Y->n - 1; i > 0; i--)
		if (Y->p[i] != 0) {
			break;
		}
	i++;

	X->s = Y->s;

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i));

	memset(X->p, 0, X->n * ciL);
	memcpy(X->p, Y->p, i * ciL);

cleanup:

	return (ret);
}

/*
 * Swap the contents of X and Y
 */
void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y)
{
	mbedtls_mpi T;

	memcpy(&T, X, sizeof(mbedtls_mpi));
	memcpy(X, Y, sizeof(mbedtls_mpi));
	memcpy(Y, &T, sizeof(mbedtls_mpi));
}

/*
 * Conditionally assign X = Y, without leaking information
 * about whether the assignment was made or not.
 * (Leaking information about the respective sizes of X and Y is ok however.)
 */
int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign)
{
	int ret = 0;
	size_t i;

	/* make sure assign is 0 or 1 in a time-constant manner */
	assign = (assign | (unsigned char) - assign) >> 7;

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));

	X->s = X->s * (1 - assign) + Y->s * assign;

	for (i = 0; i < Y->n; i++) {
		X->p[i] = X->p[i] * (1 - assign) + Y->p[i] * assign;
	}

	for (; i < X->n; i++) {
		X->p[i] *= (1 - assign);
	}

cleanup:
	return (ret);
}

/*
 * Conditionally swap X and Y, without leaking information
 * about whether the swap was made or not.
 * Here it is not ok to simply swap the pointers, which whould lead to
 * different memory access patterns when X and Y are used afterwards.
 */
int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap)
{
	int ret, s;
	size_t i;
	mbedtls_mpi_uint tmp;

	if (X == Y) {
		return (0);
	}

	/* make sure swap is 0 or 1 in a time-constant manner */
	swap = (swap | (unsigned char) - swap) >> 7;

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n));
	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Y, X->n));

	s = X->s;
	X->s = X->s * (1 - swap) + Y->s * swap;
	Y->s = Y->s * (1 - swap) + s * swap;

	for (i = 0; i < X->n; i++) {
		tmp = X->p[i];
		X->p[i] = X->p[i] * (1 - swap) + Y->p[i] * swap;
		Y->p[i] = Y->p[i] * (1 - swap) + tmp * swap;
	}

cleanup:
	return (ret);
}

/*
 * Set value from integer
 */
int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z)
{
	int ret;

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, 1));
	memset(X->p, 0, X->n * ciL);

	X->p[0] = (z < 0) ? -z : z;
	X->s = (z < 0) ? -1 : 1;

cleanup:

	return (ret);
}

/*
 * Get a specific bit
 */
int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos)
{
	if (X->n * biL <= pos) {
		return (0);
	}

	return ((X->p[pos / biL] >> (pos % biL)) & 0x01);
}

/*
 * Set a bit to a specific value of 0 or 1
 */
int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val)
{
	int ret = 0;
	size_t off = pos / biL;
	size_t idx = pos % biL;

	if (val != 0 && val != 1) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	if (X->n * biL <= pos) {
		if (val == 0) {
			return (0);
		}

		MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, off + 1));
	}

	X->p[off] &= ~((mbedtls_mpi_uint) 0x01 << idx);
	X->p[off] |= (mbedtls_mpi_uint) val << idx;

cleanup:

	return (ret);
}

/*
 * Return the number of less significant zero-bits
 */
size_t mbedtls_mpi_lsb(const mbedtls_mpi *X)
{
	size_t i, j, count = 0;

	for (i = 0; i < X->n; i++)
		for (j = 0; j < biL; j++, count++)
			if (((X->p[i] >> j) & 1) != 0) {
				return (count);
			}

	return (0);
}

/*
 * Count leading zero bits in a given integer
 */
static size_t mbedtls_clz(const mbedtls_mpi_uint x)
{
	size_t j;
	mbedtls_mpi_uint mask = (mbedtls_mpi_uint) 1 << (biL - 1);

	for (j = 0; j < biL; j++) {
		if (x & mask) {
			break;
		}

		mask >>= 1;
	}

	return j;
}

/*
 * Return the number of bits
 */
size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X)
{
	size_t i, j;

	if (X->n == 0) {
		return (0);
	}

	for (i = X->n - 1; i > 0; i--)
		if (X->p[i] != 0) {
			break;
		}

	j = biL - mbedtls_clz(X->p[i]);

	return ((i * biL) + j);
}

/*
 * Return the total size in bytes
 */
size_t mbedtls_mpi_size(const mbedtls_mpi *X)
{
	return ((mbedtls_mpi_bitlen(X) + 7) >> 3);
}

/*
 * Convert an ASCII character to digit value
 */
static int mpi_get_digit(mbedtls_mpi_uint *d, int radix, char c)
{
	*d = 255;

	if (c >= 0x30 && c <= 0x39) {
		*d = c - 0x30;
	}
	if (c >= 0x41 && c <= 0x46) {
		*d = c - 0x37;
	}
	if (c >= 0x61 && c <= 0x66) {
		*d = c - 0x57;
	}

	if (*d >= (mbedtls_mpi_uint) radix) {
		return (MBEDTLS_ERR_MPI_INVALID_CHARACTER);
	}

	return (0);
}

/*
 * Import from an ASCII string
 */
int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s)
{
	int ret;
	size_t i, j, slen, n;
	mbedtls_mpi_uint d;
	mbedtls_mpi T;

	if (radix < 2 || radix > 16) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	mbedtls_mpi_init(&T);

	slen = strlen(s);

	if (radix == 16) {
		if (slen > MPI_SIZE_T_MAX >> 2) {
			return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
		}

		n = BITS_TO_LIMBS(slen << 2);

		MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, n));
		MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));

		for (i = slen, j = 0; i > 0; i--, j++) {
			if (i == 1 && s[i - 1] == '-') {
				X->s = -1;
				break;
			}

			MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i - 1]));
			X->p[j / (2 * ciL)] |= d << ((j % (2 * ciL)) << 2);
		}
	} else {
		MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));

		for (i = 0; i < slen; i++) {
			if (i == 0 && s[i] == '-') {
				X->s = -1;
				continue;
			}

			MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i]));
			MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T, X, radix));

			if (X->s == 1) {
				MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, &T, d));
			} else {
				MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(X, &T, d));
			}
		}
	}

cleanup:

	mbedtls_mpi_free(&T);

	return (ret);
}

/*
 * Helper to write the digits high-order first
 */
static int mpi_write_hlp(mbedtls_mpi *X, int radix, char **p)
{
	int ret;
	mbedtls_mpi_uint r;

	if (radix < 2 || radix > 16) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, radix));
	MBEDTLS_MPI_CHK(mbedtls_mpi_div_int(X, NULL, X, radix));

	if (mbedtls_mpi_cmp_int(X, 0) != 0) {
		MBEDTLS_MPI_CHK(mpi_write_hlp(X, radix, p));
	}

	if (r < 10) {
		*(*p)++ = (char)(r + 0x30);
	} else {
		*(*p)++ = (char)(r + 0x37);
	}

cleanup:

	return (ret);
}

/*
 * Export into an ASCII string
 */
int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix, char *buf, size_t buflen, size_t *olen)
{
	int ret = 0;
	size_t n;
	char *p;
	mbedtls_mpi T;

	if (radix < 2 || radix > 16) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	n = mbedtls_mpi_bitlen(X);
	if (radix >= 4) {
		n >>= 1;
	}
	if (radix >= 16) {
		n >>= 1;
	}
	n += 3;

	if (buflen < n) {
		*olen = n;
		return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
	}

	p = buf;
	mbedtls_mpi_init(&T);

	if (X->s == -1) {
		*p++ = '-';
	}

	if (radix == 16) {
		int c;
		size_t i, j, k;

		for (i = X->n, k = 0; i > 0; i--) {
			for (j = ciL; j > 0; j--) {
				c = (X->p[i - 1] >> ((j - 1) << 3)) & 0xFF;

				if (c == 0 && k == 0 && (i + j) != 2) {
					continue;
				}

				*(p++) = "0123456789ABCDEF"[c / 16];
				*(p++) = "0123456789ABCDEF"[c % 16];
				k = 1;
			}
		}
	} else {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T, X));

		if (T.s == -1) {
			T.s = 1;
		}

		MBEDTLS_MPI_CHK(mpi_write_hlp(&T, radix, &p));
	}

	*p++ = '\0';
	*olen = p - buf;

cleanup:

	mbedtls_mpi_free(&T);

	return (ret);
}

#if defined(MBEDTLS_FS_IO)
/*
 * Read X from an opened file
 */
int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin)
{
	mbedtls_mpi_uint d;
	size_t slen;
	char *p;
	/*
	 * Buffer should have space for (short) label and decimal formatted MPI,
	 * newline characters and '\0'
	 */
	char s[MBEDTLS_MPI_RW_BUFFER_SIZE];

	memset(s, 0, sizeof(s));
	if (fgets(s, sizeof(s) - 1, fin) == NULL) {
		return (MBEDTLS_ERR_MPI_FILE_IO_ERROR);
	}

	slen = strlen(s);
	if (slen == sizeof(s) - 2) {
		return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
	}

	if (s[slen - 1] == '\n') {
		slen--;
		s[slen] = '\0';
	}
	if (s[slen - 1] == '\r') {
		slen--;
		s[slen] = '\0';
	}

	p = s + slen;
	while (--p >= s)
		if (mpi_get_digit(&d, radix, *p) != 0) {
			break;
		}

	return (mbedtls_mpi_read_string(X, radix, p + 1));
}

/*
 * Write X into an opened file (or stdout if fout == NULL)
 */
int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X, int radix, FILE *fout)
{
	int ret;
	size_t n, slen, plen;
	/*
	 * Buffer should have space for (short) label and decimal formatted MPI,
	 * newline characters and '\0'
	 */
	char s[MBEDTLS_MPI_RW_BUFFER_SIZE];

	memset(s, 0, sizeof(s));

	MBEDTLS_MPI_CHK(mbedtls_mpi_write_string(X, radix, s, sizeof(s) - 2, &n));

	if (p == NULL) {
		p = "";
	}

	plen = strlen(p);
	slen = strlen(s);
	s[slen++] = '\r';
	s[slen++] = '\n';

	if (fout != NULL) {
		if (fwrite(p, 1, plen, fout) != plen || fwrite(s, 1, slen, fout) != slen) {
			return (MBEDTLS_ERR_MPI_FILE_IO_ERROR);
		}
	} else {
		mbedtls_printf("%s%s", p, s);
	}

cleanup:

	return (ret);
}
#endif							/* MBEDTLS_FS_IO */

/*
 * Import X from unsigned binary data, big endian
 */
int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
{
	int ret;
	size_t i, j, n;

	for (n = 0; n < buflen; n++)
		if (buf[n] != 0) {
			break;
		}

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, CHARS_TO_LIMBS(buflen - n)));
	MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));

	for (i = buflen, j = 0; i > n; i--, j++) {
		X->p[j / ciL] |= ((mbedtls_mpi_uint) buf[i - 1]) << ((j % ciL) << 3);
	}

cleanup:

	return (ret);
}

/*
 * Export X into unsigned binary data, big endian
 */
int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf, size_t buflen)
{
	size_t i, j, n;

	n = mbedtls_mpi_size(X);

	if (buflen < n) {
		return (MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL);
	}

	memset(buf, 0, buflen);

	for (i = buflen - 1, j = 0; n > 0; i--, j++, n--) {
		buf[i] = (unsigned char)(X->p[j / ciL] >> ((j % ciL) << 3));
	}

	return (0);
}

/*
 * Left-shift: X <<= count
 */
int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count)
{
	int ret;
	size_t i, v0, t1;
	mbedtls_mpi_uint r0 = 0, r1;

	v0 = count / (biL);
	t1 = count & (biL - 1);

	i = mbedtls_mpi_bitlen(X) + count;

	if (X->n * biL < i) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, BITS_TO_LIMBS(i)));
	}

	ret = 0;

	/*
	 * shift by count / limb_size
	 */
	if (v0 > 0) {
		for (i = X->n; i > v0; i--) {
			X->p[i - 1] = X->p[i - v0 - 1];
		}

		for (; i > 0; i--) {
			X->p[i - 1] = 0;
		}
	}

	/*
	 * shift by count % limb_size
	 */
	if (t1 > 0) {
		for (i = v0; i < X->n; i++) {
			r1 = X->p[i] >> (biL - t1);
			X->p[i] <<= t1;
			X->p[i] |= r0;
			r0 = r1;
		}
	}

cleanup:

	return (ret);
}

/*
 * Right-shift: X >>= count
 */
int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count)
{
	size_t i, v0, v1;
	mbedtls_mpi_uint r0 = 0, r1;

	v0 = count / biL;
	v1 = count & (biL - 1);

	if (v0 > X->n || (v0 == X->n && v1 > 0)) {
		return mbedtls_mpi_lset(X, 0);
	}

	/*
	 * shift by count / limb_size
	 */
	if (v0 > 0) {
		for (i = 0; i < X->n - v0; i++) {
			X->p[i] = X->p[i + v0];
		}

		for (; i < X->n; i++) {
			X->p[i] = 0;
		}
	}

	/*
	 * shift by count % limb_size
	 */
	if (v1 > 0) {
		for (i = X->n; i > 0; i--) {
			r1 = X->p[i - 1] << (biL - v1);
			X->p[i - 1] >>= v1;
			X->p[i - 1] |= r0;
			r0 = r1;
		}
	}

	return (0);
}

/*
 * Compare unsigned values
 */
int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y)
{
	size_t i, j;

	for (i = X->n; i > 0; i--)
		if (X->p[i - 1] != 0) {
			break;
		}

	for (j = Y->n; j > 0; j--)
		if (Y->p[j - 1] != 0) {
			break;
		}

	if (i == 0 && j == 0) {
		return (0);
	}

	if (i > j) {
		return (1);
	}
	if (j > i) {
		return (-1);
	}

	for (; i > 0; i--) {
		if (X->p[i - 1] > Y->p[i - 1]) {
			return (1);
		}
		if (X->p[i - 1] < Y->p[i - 1]) {
			return (-1);
		}
	}

	return (0);
}

/*
 * Compare signed values
 */
int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y)
{
	size_t i, j;

	for (i = X->n; i > 0; i--)
		if (X->p[i - 1] != 0) {
			break;
		}

	for (j = Y->n; j > 0; j--)
		if (Y->p[j - 1] != 0) {
			break;
		}

	if (i == 0 && j == 0) {
		return (0);
	}

	if (i > j) {
		return (X->s);
	}
	if (j > i) {
		return (-Y->s);
	}

	if (X->s > 0 && Y->s < 0) {
		return (1);
	}
	if (Y->s > 0 && X->s < 0) {
		return (-1);
	}

	for (; i > 0; i--) {
		if (X->p[i - 1] > Y->p[i - 1]) {
			return (X->s);
		}
		if (X->p[i - 1] < Y->p[i - 1]) {
			return (-X->s);
		}
	}

	return (0);
}

/*
 * Compare signed values
 */
int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z)
{
	mbedtls_mpi Y;
	mbedtls_mpi_uint p[1];

	*p = (z < 0) ? -z : z;
	Y.s = (z < 0) ? -1 : 1;
	Y.n = 1;
	Y.p = p;

	return (mbedtls_mpi_cmp_mpi(X, &Y));
}

/*
 * Unsigned addition: X = |A| + |B|  (HAC 14.7)
 */
int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	int ret;
	size_t i, j;
	mbedtls_mpi_uint *o, *p, c, tmp;

	if (X == B) {
		const mbedtls_mpi *T = A;
		A = X;
		B = T;
	}

	if (X != A) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A));
	}

	/*
	 * X should always be positive as a result of unsigned additions.
	 */
	X->s = 1;

	for (j = B->n; j > 0; j--)
		if (B->p[j - 1] != 0) {
			break;
		}

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j));

	o = B->p;
	p = X->p;
	c = 0;

	/*
	 * tmp is used because it might happen that p == o
	 */
	for (i = 0; i < j; i++, o++, p++) {
		tmp = *o;
		*p += c;
		c = (*p < c);
		*p += tmp;
		c += (*p < tmp);
	}

	while (c != 0) {
		if (i >= X->n) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i + 1));
			p = X->p + i;
		}

		*p += c;
		c = (*p < c);
		i++;
		p++;
	}

cleanup:

	return (ret);
}

/*
 * Helper for mbedtls_mpi subtraction
 */
static void mpi_sub_hlp(size_t n, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d)
{
	size_t i;
	mbedtls_mpi_uint c, z;

	for (i = c = 0; i < n; i++, s++, d++) {
		z = (*d < c);
		*d -= c;
		c = (*d < *s) + z;
		*d -= *s;
	}

	while (c != 0) {
		z = (*d < c);
		*d -= c;
		c = z;
		i++;
		d++;
	}
}

/*
 * Unsigned subtraction: X = |A| - |B|  (HAC 14.9)
 */
int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	mbedtls_mpi TB;
	int ret;
	size_t n;

	if (mbedtls_mpi_cmp_abs(A, B) < 0) {
		return (MBEDTLS_ERR_MPI_NEGATIVE_VALUE);
	}

	mbedtls_mpi_init(&TB);

	if (X == B) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B));
		B = &TB;
	}

	if (X != A) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A));
	}

	/*
	 * X should always be positive as a result of unsigned subtractions.
	 */
	X->s = 1;

	ret = 0;

	for (n = B->n; n > 0; n--)
		if (B->p[n - 1] != 0) {
			break;
		}

	mpi_sub_hlp(n, B->p, X->p);

cleanup:

	mbedtls_mpi_free(&TB);

	return (ret);
}

/*
 * Signed addition: X = A + B
 */
int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	int ret, s = A->s;

	if (A->s * B->s < 0) {
		if (mbedtls_mpi_cmp_abs(A, B) >= 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, A, B));
			X->s = s;
		} else {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, B, A));
			X->s = -s;
		}
	} else {
		MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(X, A, B));
		X->s = s;
	}

cleanup:

	return (ret);
}

/*
 * Signed subtraction: X = A - B
 */
int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	int ret, s = A->s;

	if (A->s * B->s > 0) {
		if (mbedtls_mpi_cmp_abs(A, B) >= 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, A, B));
			X->s = s;
		} else {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, B, A));
			X->s = -s;
		}
	} else {
		MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(X, A, B));
		X->s = s;
	}

cleanup:

	return (ret);
}

/*
 * Signed addition: X = A + b
 */
int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b)
{
	mbedtls_mpi _B;
	mbedtls_mpi_uint p[1];

	p[0] = (b < 0) ? -b : b;
	_B.s = (b < 0) ? -1 : 1;
	_B.n = 1;
	_B.p = p;

	return (mbedtls_mpi_add_mpi(X, A, &_B));
}

/*
 * Signed subtraction: X = A - b
 */
int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b)
{
	mbedtls_mpi _B;
	mbedtls_mpi_uint p[1];

	p[0] = (b < 0) ? -b : b;
	_B.s = (b < 0) ? -1 : 1;
	_B.n = 1;
	_B.p = p;

	return (mbedtls_mpi_sub_mpi(X, A, &_B));
}

/*
 * Helper for mbedtls_mpi multiplication
 */
static
#if defined(__APPLE__) && defined(__arm__)
/*
 * Apple LLVM version 4.2 (clang-425.0.24) (based on LLVM 3.2svn)
 * appears to need this to prevent bad ARM code generation at -O3.
 */
__attribute__((noinline))
#endif
void mpi_mul_hlp(size_t i, mbedtls_mpi_uint *s, mbedtls_mpi_uint *d, mbedtls_mpi_uint b)
{
	mbedtls_mpi_uint c = 0, t = 0;

#if defined(MULADDC_HUIT)
	for (; i >= 8; i -= 8) {
		MULADDC_INIT MULADDC_HUIT MULADDC_STOP
	}
	for (; i > 0; i--) {
		MULADDC_INIT MULADDC_CORE MULADDC_STOP
	}
#else							/* MULADDC_HUIT */
	for (; i >= 16; i -= 16) {
		MULADDC_INIT MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_STOP
	}
	for (; i >= 8; i -= 8) {
		MULADDC_INIT MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_CORE MULADDC_STOP
	}
	for (; i > 0; i--) {
		MULADDC_INIT MULADDC_CORE MULADDC_STOP
	}
#endif							/* MULADDC_HUIT */
	t++;

	do {
		*d += c;
		c = (*d < c);
		d++;
	} while (c != 0);
}

/*
 * Baseline multiplication: X = A * B  (HAC 14.12)
 */
int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	int ret;
	size_t i, j;
	mbedtls_mpi TA, TB;

	mbedtls_mpi_init(&TA);
	mbedtls_mpi_init(&TB);

	if (X == A) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TA, A));
		A = &TA;
	}
	if (X == B) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B));
		B = &TB;
	}

	for (i = A->n; i > 0; i--)
		if (A->p[i - 1] != 0) {
			break;
		}

	for (j = B->n; j > 0; j--)
		if (B->p[j - 1] != 0) {
			break;
		}

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i + j));
	MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0));

	for (i++; j > 0; j--) {
		mpi_mul_hlp(i - 1, A->p, X->p + j - 1, B->p[j - 1]);
	}

	X->s = A->s * B->s;

cleanup:

	mbedtls_mpi_free(&TB);
	mbedtls_mpi_free(&TA);

	return (ret);
}

/*
 * Baseline multiplication: X = A * b
 */
int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b)
{
	mbedtls_mpi _B;
	mbedtls_mpi_uint p[1];

	_B.s = 1;
	_B.n = 1;
	_B.p = p;
	p[0] = b;

	return (mbedtls_mpi_mul_mpi(X, A, &_B));
}

/*
 * Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and
 * mbedtls_mpi_uint divisor, d
 */
static mbedtls_mpi_uint mbedtls_int_div_int(mbedtls_mpi_uint u1, mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r)
{
#if defined(MBEDTLS_HAVE_UDBL)
	mbedtls_t_udbl dividend, quotient;
#else
	const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH;
	const mbedtls_mpi_uint uint_halfword_mask = ((mbedtls_mpi_uint) 1 << biH) - 1;
	mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient;
	mbedtls_mpi_uint u0_msw, u0_lsw;
	size_t s;
#endif

	/*
	 * Check for overflow
	 */
	if (0 == d || u1 >= d) {
		if (r != NULL) {
			*r = ~0;
		}

		return (~0);
	}
#if defined(MBEDTLS_HAVE_UDBL)
	dividend = (mbedtls_t_udbl) u1 << biL;
	dividend |= (mbedtls_t_udbl) u0;
	quotient = dividend / d;
	if (quotient > ((mbedtls_t_udbl) 1 << biL) - 1) {
		quotient = ((mbedtls_t_udbl) 1 << biL) - 1;
	}

	if (r != NULL) {
		*r = (mbedtls_mpi_uint)(dividend - (quotient * d));
	}

	return (mbedtls_mpi_uint) quotient;
#else

	/*
	 * Algorithm D, Section 4.3.1 - The Art of Computer Programming
	 *   Vol. 2 - Seminumerical Algorithms, Knuth
	 */

	/*
	 * Normalize the divisor, d, and dividend, u0, u1
	 */
	s = mbedtls_clz(d);
	d = d << s;

	u1 = u1 << s;
	u1 |= (u0 >> (biL - s)) & (-(mbedtls_mpi_sint) s >> (biL - 1));
	u0 = u0 << s;

	d1 = d >> biH;
	d0 = d & uint_halfword_mask;

	u0_msw = u0 >> biH;
	u0_lsw = u0 & uint_halfword_mask;

	/*
	 * Find the first quotient and remainder
	 */
	q1 = u1 / d1;
	r0 = u1 - d1 * q1;

	while (q1 >= radix || (q1 * d0 > radix * r0 + u0_msw)) {
		q1 -= 1;
		r0 += d1;

		if (r0 >= radix) {
			break;
		}
	}

	rAX = (u1 * radix) + (u0_msw - q1 * d);
	q0 = rAX / d1;
	r0 = rAX - q0 * d1;

	while (q0 >= radix || (q0 * d0 > radix * r0 + u0_lsw)) {
		q0 -= 1;
		r0 += d1;

		if (r0 >= radix) {
			break;
		}
	}

	if (r != NULL) {
		*r = (rAX * radix + u0_lsw - q0 * d) >> s;
	}

	quotient = q1 * radix + q0;

	return quotient;
#endif
}

/*
 * Division by mbedtls_mpi: A = Q * B + R  (HAC 14.20)
 */
int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	int ret;
	size_t i, n, t, k;
	mbedtls_mpi X, Y, Z, T1, T2;

	if (mbedtls_mpi_cmp_int(B, 0) == 0) {
		return (MBEDTLS_ERR_MPI_DIVISION_BY_ZERO);
	}

	mbedtls_mpi_init(&X);
	mbedtls_mpi_init(&Y);
	mbedtls_mpi_init(&Z);
	mbedtls_mpi_init(&T1);
	mbedtls_mpi_init(&T2);

	if (mbedtls_mpi_cmp_abs(A, B) < 0) {
		if (Q != NULL) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_lset(Q, 0));
		}
		if (R != NULL) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, A));
		}
		return (0);
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&X, A));
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Y, B));
	X.s = Y.s = 1;

	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&Z, A->n + 2));
	MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&Z, 0));
	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T1, 2));
	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T2, 3));

	k = mbedtls_mpi_bitlen(&Y) % biL;
	if (k < biL - 1) {
		k = biL - 1 - k;
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&X, k));
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, k));
	} else {
		k = 0;
	}

	n = X.n - 1;
	t = Y.n - 1;
	MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, biL * (n - t)));

	while (mbedtls_mpi_cmp_mpi(&X, &Y) >= 0) {
		Z.p[n - t]++;
		MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&X, &X, &Y));
	}
	MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&Y, biL * (n - t)));

	for (i = n; i > t; i--) {
		if (X.p[i] >= Y.p[t]) {
			Z.p[i - t - 1] = ~0;
		} else {
			Z.p[i - t - 1] = mbedtls_int_div_int(X.p[i], X.p[i - 1], Y.p[t], NULL);
		}

		Z.p[i - t - 1]++;
		do {
			Z.p[i - t - 1]--;

			MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&T1, 0));
			T1.p[0] = (t < 1) ? 0 : Y.p[t - 1];
			T1.p[1] = Y.p[t];
			MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T1, &T1, Z.p[i - t - 1]));

			MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&T2, 0));
			T2.p[0] = (i < 2) ? 0 : X.p[i - 2];
			T2.p[1] = (i < 1) ? 0 : X.p[i - 1];
			T2.p[2] = X.p[i];
		} while (mbedtls_mpi_cmp_mpi(&T1, &T2) > 0);

		MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T1, &Y, Z.p[i - t - 1]));
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1)));
		MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&X, &X, &T1));

		if (mbedtls_mpi_cmp_int(&X, 0) < 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T1, &Y));
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1)));
			MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&X, &X, &T1));
			Z.p[i - t - 1]--;
		}
	}

	if (Q != NULL) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(Q, &Z));
		Q->s = A->s * B->s;
	}

	if (R != NULL) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&X, k));
		X.s = A->s;
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, &X));

		if (mbedtls_mpi_cmp_int(R, 0) == 0) {
			R->s = 1;
		}
	}

cleanup:

	mbedtls_mpi_free(&X);
	mbedtls_mpi_free(&Y);
	mbedtls_mpi_free(&Z);
	mbedtls_mpi_free(&T1);
	mbedtls_mpi_free(&T2);

	return (ret);
}

/*
 * Division by int: A = Q * b + R
 */
int mbedtls_mpi_div_int(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b)
{
	mbedtls_mpi _B;
	mbedtls_mpi_uint p[1];

	p[0] = (b < 0) ? -b : b;
	_B.s = (b < 0) ? -1 : 1;
	_B.n = 1;
	_B.p = p;

	return (mbedtls_mpi_div_mpi(Q, R, A, &_B));
}

/*
 * Modulo: R = A mod B
 */
int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	int ret;

	if (mbedtls_mpi_cmp_int(B, 0) < 0) {
		return (MBEDTLS_ERR_MPI_NEGATIVE_VALUE);
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_div_mpi(NULL, R, A, B));

	while (mbedtls_mpi_cmp_int(R, 0) < 0) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(R, R, B));
	}

	while (mbedtls_mpi_cmp_mpi(R, B) >= 0) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(R, R, B));
	}

cleanup:

	return (ret);
}

/*
 * Modulo: r = A mod b
 */
int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b)
{
	size_t i;
	mbedtls_mpi_uint x, y, z;

	if (b == 0) {
		return (MBEDTLS_ERR_MPI_DIVISION_BY_ZERO);
	}

	if (b < 0) {
		return (MBEDTLS_ERR_MPI_NEGATIVE_VALUE);
	}

	/*
	 * handle trivial cases
	 */
	if (b == 1) {
		*r = 0;
		return (0);
	}

	if (b == 2) {
		*r = A->p[0] & 1;
		return (0);
	}

	/*
	 * general case
	 */
	for (i = A->n, y = 0; i > 0; i--) {
		x = A->p[i - 1];
		y = (y << biH) | (x >> biH);
		z = y / b;
		y -= z * b;

		x <<= biH;
		y = (y << biH) | (x >> biH);
		z = y / b;
		y -= z * b;
	}

	/*
	 * If A is negative, then the current y represents a negative value.
	 * Flipping it to the positive side.
	 */
	if (A->s < 0 && y != 0) {
		y = b - y;
	}

	*r = y;

	return (0);
}

/*
 * Fast Montgomery initialization (thanks to Tom St Denis)
 */
static void mpi_montg_init(mbedtls_mpi_uint *mm, const mbedtls_mpi *N)
{
	mbedtls_mpi_uint x, m0 = N->p[0];
	unsigned int i;

	x = m0;
	x += ((m0 + 2) & 4) << 1;

	for (i = biL; i >= 8; i /= 2) {
		x *= (2 - (m0 * x));
	}

	*mm = ~x + 1;
}

/*
 * Montgomery multiplication: A = A * B * R^-1 mod N  (HAC 14.36)
 */
static int mpi_montmul(mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T)
{
	size_t i, n, m;
	mbedtls_mpi_uint u0, u1, *d;

	if (T->n < N->n + 1 || T->p == NULL) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	memset(T->p, 0, T->n * ciL);

	d = T->p;
	n = N->n;
	m = (B->n < n) ? B->n : n;

	for (i = 0; i < n; i++) {
		/*
		 * T = (T + u0*B + u1*N) / 2^biL
		 */
		u0 = A->p[i];
		u1 = (d[0] + u0 * B->p[0]) * mm;

		mpi_mul_hlp(m, B->p, d, u0);
		mpi_mul_hlp(n, N->p, d, u1);

		*d++ = u0;
		d[n + 1] = 0;
	}

	memcpy(A->p, d, (n + 1) * ciL);

	if (mbedtls_mpi_cmp_abs(A, N) >= 0) {
		mpi_sub_hlp(n, N->p, A->p);
	} else
		/* prevent timing attacks */
	{
		mpi_sub_hlp(n, A->p, T->p);
	}

	return (0);
}

/*
 * Montgomery reduction: A = A * R^-1 mod N
 */
static int mpi_montred(mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T)
{
	mbedtls_mpi_uint z = 1;
	mbedtls_mpi U;

	U.n = U.s = (int)z;
	U.p = &z;

	return (mpi_montmul(A, &U, N, mm, T));
}

/*
 * Sliding-window exponentiation: X = A^E mod N  (HAC 14.85)
 */
int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR)
{
	int ret;
	size_t wbits, wsize, one = 1;
	size_t i, j, nblimbs;
	size_t bufsize, nbits;
	mbedtls_mpi_uint ei, mm, state;
	mbedtls_mpi RR, T, W[2 << MBEDTLS_MPI_WINDOW_SIZE], Apos;
	int neg;

	if (mbedtls_mpi_cmp_int(N, 0) < 0 || (N->p[0] & 1) == 0) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	if (mbedtls_mpi_cmp_int(E, 0) < 0) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	/*
	 * Init temps and window size
	 */
	mpi_montg_init(&mm, N);
	mbedtls_mpi_init(&RR);
	mbedtls_mpi_init(&T);
	mbedtls_mpi_init(&Apos);
	memset(W, 0, sizeof(W));

	i = mbedtls_mpi_bitlen(E);

	wsize = (i > 671) ? 6 : (i > 239) ? 5 : (i > 79) ? 4 : (i > 23) ? 3 : 1;

	if (wsize > MBEDTLS_MPI_WINDOW_SIZE) {
		wsize = MBEDTLS_MPI_WINDOW_SIZE;
	}

	j = N->n + 1;
	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j));
	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[1], j));
	MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T, j * 2));

	/*
	 * Compensate for negative A (and correct at the end)
	 */
	neg = (A->s == -1);
	if (neg) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Apos, A));
		Apos.s = 1;
		A = &Apos;
	}

	/*
	 * If 1st call, pre-compute R^2 mod N
	 */
	if (_RR == NULL || _RR->p == NULL) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&RR, 1));
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&RR, N->n * 2 * biL));
		MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&RR, &RR, N));

		if (_RR != NULL) {
			memcpy(_RR, &RR, sizeof(mbedtls_mpi));
		}
	} else {
		memcpy(&RR, _RR, sizeof(mbedtls_mpi));
	}

	/*
	 * W[1] = A * R^2 * R^-1 mod N = A * R mod N
	 */
	if (mbedtls_mpi_cmp_mpi(A, N) >= 0) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&W[1], A, N));
	} else {
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[1], A));
	}

	MBEDTLS_MPI_CHK(mpi_montmul(&W[1], &RR, N, mm, &T));

	/*
	 * X = R^2 * R^-1 mod N = R mod N
	 */
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &RR));
	MBEDTLS_MPI_CHK(mpi_montred(X, N, mm, &T));

	if (wsize > 1) {
		/*
		 * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1)
		 */
		j = one << (wsize - 1);

		MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[j], N->n + 1));
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[j], &W[1]));

		for (i = 0; i < wsize - 1; i++) {
			MBEDTLS_MPI_CHK(mpi_montmul(&W[j], &W[j], N, mm, &T));
		}

		/*
		 * W[i] = W[i - 1] * W[1]
		 */
		for (i = j + 1; i < (one << wsize); i++) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[i], N->n + 1));
			MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[i], &W[i - 1]));

			MBEDTLS_MPI_CHK(mpi_montmul(&W[i], &W[1], N, mm, &T));
		}
	}

	nblimbs = E->n;
	bufsize = 0;
	nbits = 0;
	wbits = 0;
	state = 0;

	while (1) {
		if (bufsize == 0) {
			if (nblimbs == 0) {
				break;
			}

			nblimbs--;

			bufsize = sizeof(mbedtls_mpi_uint) << 3;
		}

		bufsize--;

		ei = (E->p[nblimbs] >> bufsize) & 1;

		/*
		 * skip leading 0s
		 */
		if (ei == 0 && state == 0) {
			continue;
		}

		if (ei == 0 && state == 1) {
			/*
			 * out of window, square X
			 */
			MBEDTLS_MPI_CHK(mpi_montmul(X, X, N, mm, &T));
			continue;
		}

		/*
		 * add ei to current window
		 */
		state = 2;

		nbits++;
		wbits |= (ei << (wsize - nbits));

		if (nbits == wsize) {
			/*
			 * X = X^wsize R^-1 mod N
			 */
			for (i = 0; i < wsize; i++) {
				MBEDTLS_MPI_CHK(mpi_montmul(X, X, N, mm, &T));
			}

			/*
			 * X = X * W[wbits] R^-1 mod N
			 */
			MBEDTLS_MPI_CHK(mpi_montmul(X, &W[wbits], N, mm, &T));

			state--;
			nbits = 0;
			wbits = 0;
		}
	}

	/*
	 * process the remaining bits
	 */
	for (i = 0; i < nbits; i++) {
		MBEDTLS_MPI_CHK(mpi_montmul(X, X, N, mm, &T));

		wbits <<= 1;

		if ((wbits & (one << wsize)) != 0) {
			MBEDTLS_MPI_CHK(mpi_montmul(X, &W[1], N, mm, &T));
		}
	}

	/*
	 * X = A^E * R * R^-1 mod N = A^E mod N
	 */
	MBEDTLS_MPI_CHK(mpi_montred(X, N, mm, &T));

	if (neg) {
		X->s = -1;
		MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, N, X));
	}

cleanup:

	for (i = (one << (wsize - 1)); i < (one << wsize); i++) {
		mbedtls_mpi_free(&W[i]);
	}

	mbedtls_mpi_free(&W[1]);
	mbedtls_mpi_free(&T);
	mbedtls_mpi_free(&Apos);

	if (_RR == NULL || _RR->p == NULL) {
		mbedtls_mpi_free(&RR);
	}

	return (ret);
}

/*
 * Greatest common divisor: G = gcd(A, B)  (HAC 14.54)
 */
int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B)
{
	int ret;
	size_t lz, lzt;
	mbedtls_mpi TG, TA, TB;

	mbedtls_mpi_init(&TG);
	mbedtls_mpi_init(&TA);
	mbedtls_mpi_init(&TB);

	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TA, A));
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B));

	lz = mbedtls_mpi_lsb(&TA);
	lzt = mbedtls_mpi_lsb(&TB);

	if (lzt < lz) {
		lz = lzt;
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, lz));
	MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, lz));

	TA.s = TB.s = 1;

	while (mbedtls_mpi_cmp_int(&TA, 0) != 0) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, mbedtls_mpi_lsb(&TA)));
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, mbedtls_mpi_lsb(&TB)));

		if (mbedtls_mpi_cmp_mpi(&TA, &TB) >= 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&TA, &TA, &TB));
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, 1));
		} else {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&TB, &TB, &TA));
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, 1));
		}
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&TB, lz));
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(G, &TB));

cleanup:

	mbedtls_mpi_free(&TG);
	mbedtls_mpi_free(&TA);
	mbedtls_mpi_free(&TB);

	return (ret);
}

/*
 * Fill X with size bytes of random.
 *
 * Use a temporary bytes representation to make sure the result is the same
 * regardless of the platform endianness (useful when f_rng is actually
 * deterministic, eg for tests).
 */
int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
	int ret;
	unsigned char buf[MBEDTLS_MPI_MAX_SIZE];

	if (size > MBEDTLS_MPI_MAX_SIZE) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	MBEDTLS_MPI_CHK(f_rng(p_rng, buf, size));
	MBEDTLS_MPI_CHK(mbedtls_mpi_read_binary(X, buf, size));

cleanup:
	return (ret);
}

/*
 * Modular inverse: X = A^-1 mod N  (HAC 14.61 / 14.64)
 */
int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N)
{
	int ret;
	mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2;

	if (mbedtls_mpi_cmp_int(N, 0) <= 0) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	mbedtls_mpi_init(&TA);
	mbedtls_mpi_init(&TU);
	mbedtls_mpi_init(&U1);
	mbedtls_mpi_init(&U2);
	mbedtls_mpi_init(&G);
	mbedtls_mpi_init(&TB);
	mbedtls_mpi_init(&TV);
	mbedtls_mpi_init(&V1);
	mbedtls_mpi_init(&V2);

	MBEDTLS_MPI_CHK(mbedtls_mpi_gcd(&G, A, N));

	if (mbedtls_mpi_cmp_int(&G, 1) != 0) {
		ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
		goto cleanup;
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&TA, A, N));
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TU, &TA));
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, N));
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TV, N));

	MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&U1, 1));
	MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&U2, 0));
	MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&V1, 0));
	MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&V2, 1));

	do {
		while ((TU.p[0] & 1) == 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TU, 1));

			if ((U1.p[0] & 1) != 0 || (U2.p[0] & 1) != 0) {
				MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&U1, &U1, &TB));
				MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U2, &U2, &TA));
			}

			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&U1, 1));
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&U2, 1));
		}

		while ((TV.p[0] & 1) == 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TV, 1));

			if ((V1.p[0] & 1) != 0 || (V2.p[0] & 1) != 0) {
				MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&V1, &V1, &TB));
				MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V2, &V2, &TA));
			}

			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&V1, 1));
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&V2, 1));
		}

		if (mbedtls_mpi_cmp_mpi(&TU, &TV) >= 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&TU, &TU, &TV));
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U1, &U1, &V1));
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U2, &U2, &V2));
		} else {
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&TV, &TV, &TU));
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V1, &V1, &U1));
			MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V2, &V2, &U2));
		}
	} while (mbedtls_mpi_cmp_int(&TU, 0) != 0);

	while (mbedtls_mpi_cmp_int(&V1, 0) < 0) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&V1, &V1, N));
	}

	while (mbedtls_mpi_cmp_mpi(&V1, N) >= 0) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V1, &V1, N));
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &V1));

cleanup:

	mbedtls_mpi_free(&TA);
	mbedtls_mpi_free(&TU);
	mbedtls_mpi_free(&U1);
	mbedtls_mpi_free(&U2);
	mbedtls_mpi_free(&G);
	mbedtls_mpi_free(&TB);
	mbedtls_mpi_free(&TV);
	mbedtls_mpi_free(&V1);
	mbedtls_mpi_free(&V2);

	return (ret);
}

#if defined(MBEDTLS_GENPRIME)

static const int small_prime[] = {
	3, 5, 7, 11, 13, 17, 19, 23,
	29, 31, 37, 41, 43, 47, 53, 59,
	61, 67, 71, 73, 79, 83, 89, 97,
	101, 103, 107, 109, 113, 127, 131, 137,
	139, 149, 151, 157, 163, 167, 173, 179,
	181, 191, 193, 197, 199, 211, 223, 227,
	229, 233, 239, 241, 251, 257, 263, 269,
	271, 277, 281, 283, 293, 307, 311, 313,
	317, 331, 337, 347, 349, 353, 359, 367,
	373, 379, 383, 389, 397, 401, 409, 419,
	421, 431, 433, 439, 443, 449, 457, 461,
	463, 467, 479, 487, 491, 499, 503, 509,
	521, 523, 541, 547, 557, 563, 569, 571,
	577, 587, 593, 599, 601, 607, 613, 617,
	619, 631, 641, 643, 647, 653, 659, 661,
	673, 677, 683, 691, 701, 709, 719, 727,
	733, 739, 743, 751, 757, 761, 769, 773,
	787, 797, 809, 811, 821, 823, 827, 829,
	839, 853, 857, 859, 863, 877, 881, 883,
	887, 907, 911, 919, 929, 937, 941, 947,
	953, 967, 971, 977, 983, 991, 997, -103
};

/*
 * Small divisors test (X must be positive)
 *
 * Return values:
 * 0: no small factor (possible prime, more tests needed)
 * 1: certain prime
 * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime
 * other negative: error
 */
static int mpi_check_small_factors(const mbedtls_mpi *X)
{
	int ret = 0;
	size_t i;
	mbedtls_mpi_uint r;

	if ((X->p[0] & 1) == 0) {
		return (MBEDTLS_ERR_MPI_NOT_ACCEPTABLE);
	}

	for (i = 0; small_prime[i] > 0; i++) {
		if (mbedtls_mpi_cmp_int(X, small_prime[i]) <= 0) {
			return (1);
		}

		MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, small_prime[i]));

		if (r == 0) {
			return (MBEDTLS_ERR_MPI_NOT_ACCEPTABLE);
		}
	}

cleanup:
	return (ret);
}

/*
 * Miller-Rabin pseudo-primality test  (HAC 4.24)
 */
static int mpi_miller_rabin(const mbedtls_mpi *X, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
	int ret, count;
	size_t i, j, k, n, s;
	mbedtls_mpi W, R, T, A, RR;

	mbedtls_mpi_init(&W);
	mbedtls_mpi_init(&R);
	mbedtls_mpi_init(&T);
	mbedtls_mpi_init(&A);
	mbedtls_mpi_init(&RR);

	/*
	 * W = |X| - 1
	 * R = W >> lsb( W )
	 */
	MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(&W, X, 1));
	s = mbedtls_mpi_lsb(&W);
	MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R, &W));
	MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&R, s));

	i = mbedtls_mpi_bitlen(X);
	/*
	 * HAC, table 4.4
	 */
	n = ((i >= 1300) ? 2 : (i >= 850) ? 3 : (i >= 650) ? 4 : (i >= 350) ? 8 : (i >= 250) ? 12 : (i >= 150) ? 18 : 27);

	for (i = 0; i < n; i++) {
		/*
		 * pick a random A, 1 < A < |X| - 1
		 */
		MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(&A, X->n * ciL, f_rng, p_rng));

		if (mbedtls_mpi_cmp_mpi(&A, &W) >= 0) {
			j = mbedtls_mpi_bitlen(&A) - mbedtls_mpi_bitlen(&W);
			MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&A, j + 1));
		}
		A.p[0] |= 3;

		count = 0;
		do {
			MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(&A, X->n * ciL, f_rng, p_rng));

			j = mbedtls_mpi_bitlen(&A);
			k = mbedtls_mpi_bitlen(&W);
			if (j > k) {
				MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&A, j - k));
			}

			if (count++ > 30) {
				return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
			}

		} while (mbedtls_mpi_cmp_mpi(&A, &W) >= 0 || mbedtls_mpi_cmp_int(&A, 1) <= 0);

		/*
		 * A = A^R mod |X|
		 */
		MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(&A, &A, &R, X, &RR));

		if (mbedtls_mpi_cmp_mpi(&A, &W) == 0 || mbedtls_mpi_cmp_int(&A, 1) == 0) {
			continue;
		}

		j = 1;
		while (j < s && mbedtls_mpi_cmp_mpi(&A, &W) != 0) {
			/*
			 * A = A * A mod |X|
			 */
			MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&T, &A, &A));
			MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&A, &T, X));

			if (mbedtls_mpi_cmp_int(&A, 1) == 0) {
				break;
			}

			j++;
		}

		/*
		 * not prime if A != |X| - 1 or A == 1
		 */
		if (mbedtls_mpi_cmp_mpi(&A, &W) != 0 || mbedtls_mpi_cmp_int(&A, 1) == 0) {
			ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
			break;
		}
	}

cleanup:
	mbedtls_mpi_free(&W);
	mbedtls_mpi_free(&R);
	mbedtls_mpi_free(&T);
	mbedtls_mpi_free(&A);
	mbedtls_mpi_free(&RR);

	return (ret);
}

/*
 * Pseudo-primality test: small factors, then Miller-Rabin
 */
int mbedtls_mpi_is_prime(const mbedtls_mpi *X, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
	int ret;
	mbedtls_mpi XX;

	XX.s = 1;
	XX.n = X->n;
	XX.p = X->p;

	if (mbedtls_mpi_cmp_int(&XX, 0) == 0 || mbedtls_mpi_cmp_int(&XX, 1) == 0) {
		return (MBEDTLS_ERR_MPI_NOT_ACCEPTABLE);
	}

	if (mbedtls_mpi_cmp_int(&XX, 2) == 0) {
		return (0);
	}

	if ((ret = mpi_check_small_factors(&XX)) != 0) {
		if (ret == 1) {
			return (0);
		}

		return (ret);
	}

	return (mpi_miller_rabin(&XX, f_rng, p_rng));
}

/*
 * Prime number generation
 */
int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int dh_flag, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng)
{
	int ret;
	size_t k, n;
	mbedtls_mpi_uint r;
	mbedtls_mpi Y;

	if (nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS) {
		return (MBEDTLS_ERR_MPI_BAD_INPUT_DATA);
	}

	mbedtls_mpi_init(&Y);

	n = BITS_TO_LIMBS(nbits);

	MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(X, n * ciL, f_rng, p_rng));

	k = mbedtls_mpi_bitlen(X);
	if (k > nbits) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(X, k - nbits + 1));
	}

	mbedtls_mpi_set_bit(X, nbits - 1, 1);

	X->p[0] |= 1;

	if (dh_flag == 0) {
		while ((ret = mbedtls_mpi_is_prime(X, f_rng, p_rng)) != 0) {
			if (ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) {
				goto cleanup;
			}

			MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 2));
		}
	} else {
		/*
		 * An necessary condition for Y and X = 2Y + 1 to be prime
		 * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3).
		 * Make sure it is satisfied, while keeping X = 3 mod 4
		 */

		X->p[0] |= 2;

		MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, 3));
		if (r == 0) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 8));
		} else if (r == 1) {
			MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 4));
		}

		/* Set Y = (X-1) / 2, which is X / 2 because X is odd */
		MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Y, X));
		MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&Y, 1));

		while (1) {
			/*
			 * First, check small factors for X and Y
			 * before doing Miller-Rabin on any of them
			 */
			if ((ret = mpi_check_small_factors(X)) == 0 && (ret = mpi_check_small_factors(&Y)) == 0 && (ret = mpi_miller_rabin(X, f_rng, p_rng)) == 0 && (ret = mpi_miller_rabin(&Y, f_rng, p_rng)) == 0) {
				break;
			}

			if (ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) {
				goto cleanup;
			}

			/*
			 * Next candidates. We want to preserve Y = (X-1) / 2 and
			 * Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3)
			 * so up Y by 6 and X by 12.
			 */
			MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 12));
			MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&Y, &Y, 6));
		}
	}

cleanup:

	mbedtls_mpi_free(&Y);

	return (ret);
}

#endif							/* MBEDTLS_GENPRIME */

#if defined(MBEDTLS_SELF_TEST)

#define GCD_PAIR_COUNT  3

static const int gcd_pairs[GCD_PAIR_COUNT][3] = {
	{693, 609, 21},
	{1764, 868, 28},
	{768454923, 542167814, 1}
};

/*
 * Checkup routine
 */
int mbedtls_mpi_self_test(int verbose)
{
	int ret, i;
	mbedtls_mpi A, E, N, X, Y, U, V;

	mbedtls_mpi_init(&A);
	mbedtls_mpi_init(&E);
	mbedtls_mpi_init(&N);
	mbedtls_mpi_init(&X);
	mbedtls_mpi_init(&Y);
	mbedtls_mpi_init(&U);
	mbedtls_mpi_init(&V);

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&A, 16, "EFE021C2645FD1DC586E69184AF4A31E" "D5F53E93B5F123FA41680867BA110131" "944FE7952E2517337780CB0DB80E61AA" "E7C8DDC6C5C6AADEB34EB38A2F40D5E6"));

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&E, 16, "B2E7EFD37075B9F03FF989C7C5051C20" "34D2A323810251127E7BF8625A4F49A5" "F3E27F4DA8BD59C47D6DAABA4C8127BD" "5B5C25763222FEFCCFC38B832366C29E"));

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&N, 16, "0066A198186C18C10B2F5ED9B522752A" "9830B69916E535C8F047518A889A43A5" "94B6BED27A168D31D4A52F88925AA8F5"));

	MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&X, &A, &N));

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, "602AB7ECA597A3D6B56FF9829A5E8B85" "9E857EA95A03512E2BAE7391688D264A" "A5663B0341DB9CCFD2C4C5F421FEC814" "8001B72E848A38CAE1C65F78E56ABDEF" "E12D3C039B8A02D6BE593F0BBBDA56F1" "ECF677152EF804370C1A305CAF3B5BF1" "30879B56C61DE584A0F53A2447A51E"));

	if (verbose != 0) {
		mbedtls_printf("  MPI test #1 (mul_mpi): ");
	}

	if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) {
		if (verbose != 0) {
			mbedtls_printf("failed\n");
		}

		ret = 1;
		goto cleanup;
	}

	if (verbose != 0) {
		mbedtls_printf("passed\n");
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_div_mpi(&X, &Y, &A, &N));

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, "256567336059E52CAE22925474705F39A94"));

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&V, 16, "6613F26162223DF488E9CD48CC132C7A" "0AC93C701B001B092E4E5B9F73BCD27B" "9EE50D0657C77F374E903CDFA4C642"));

	if (verbose != 0) {
		mbedtls_printf("  MPI test #2 (div_mpi): ");
	}

	if (mbedtls_mpi_cmp_mpi(&X, &U) != 0 || mbedtls_mpi_cmp_mpi(&Y, &V) != 0) {
		if (verbose != 0) {
			mbedtls_printf("failed\n");
		}

		ret = 1;
		goto cleanup;
	}

	if (verbose != 0) {
		mbedtls_printf("passed\n");
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(&X, &A, &E, &N, NULL));

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, "36E139AEA55215609D2816998ED020BB" "BD96C37890F65171D948E9BC7CBAA4D9" "325D24D6A3C12710F10A09FA08AB87"));

	if (verbose != 0) {
		mbedtls_printf("  MPI test #3 (exp_mod): ");
	}

	if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) {
		if (verbose != 0) {
			mbedtls_printf("failed\n");
		}

		ret = 1;
		goto cleanup;
	}

	if (verbose != 0) {
		mbedtls_printf("passed\n");
	}

	MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&X, &A, &N));

	MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, "003A0AAEDD7E784FC07D8F9EC6E3BFD5" "C3DBA76456363A10869622EAC2DD84EC" "C5B8A74DAC4D09E03B5E0BE779F2DF61"));

	if (verbose != 0) {
		mbedtls_printf("  MPI test #4 (inv_mod): ");
	}

	if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) {
		if (verbose != 0) {
			mbedtls_printf("failed\n");
		}

		ret = 1;
		goto cleanup;
	}

	if (verbose != 0) {
		mbedtls_printf("passed\n");
	}

	if (verbose != 0) {
		mbedtls_printf("  MPI test #5 (simple gcd): ");
	}

	for (i = 0; i < GCD_PAIR_COUNT; i++) {
		MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&X, gcd_pairs[i][0]));
		MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&Y, gcd_pairs[i][1]));

		MBEDTLS_MPI_CHK(mbedtls_mpi_gcd(&A, &X, &Y));

		if (mbedtls_mpi_cmp_int(&A, gcd_pairs[i][2]) != 0) {
			if (verbose != 0) {
				mbedtls_printf("failed at %d\n", i);
			}

			ret = 1;
			goto cleanup;
		}
	}

	if (verbose != 0) {
		mbedtls_printf("passed\n");
	}

cleanup:

	if (ret != 0 && verbose != 0) {
		mbedtls_printf("Unexpected error, return code = %08X\n", ret);
	}

	mbedtls_mpi_free(&A);
	mbedtls_mpi_free(&E);
	mbedtls_mpi_free(&N);
	mbedtls_mpi_free(&X);
	mbedtls_mpi_free(&Y);
	mbedtls_mpi_free(&U);
	mbedtls_mpi_free(&V);

	if (verbose != 0) {
		mbedtls_printf("\n");
	}

	return (ret);
}

#endif							/* MBEDTLS_SELF_TEST */

#endif							/* MBEDTLS_BIGNUM_C */
